25 June, 11:42

# You roll a die. Find each probability. (a) Rolling a 5 or a number greater than 3 (b) Rolling a number less than 4 or an even number (c) Rolling a 2 or an odd number

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1. 25 June, 12:44
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Step-by-step explanation:

Probability is expressed as

Number of possible outcomes/number of total outcome

a) A die has 6 faces and only one 5. The probability of rolling a 5 is 1/6

The probability of rolling a number greater than 3 (4, 5, 6) is 3/6 = 1/2

The events are not mutually exclusive because 5 is common to both. Therefore, The probability of rolling a 5 or a number greater than 3 is

1/6 + 1/2 - 1/6 = 1/2

b) The probability of rolling a number less than 4 (1, 2, 3) is 3/6 = 1/2

The probability of rolling an even number (2, 4, 6) is 3/6 = 1/2

The events are not mutually exclusive because 2 is common to both. Therefore, The probability of rolling a number less than 4 or an even number is is

1/2 + 1/2 - 1/6 = 5/6

c) The probability of rolling a 2 is 1/6

The probability of rolling a odd number (1, 3, 5) is 3/6 = 1/2

The events are mutually exclusive because there is no common outcome. Therefore, The probability of rolling a 2 or an odd number is is

1/6 + 1/2 = 4/6 = 2/3